Doctors treating Michael Schumacher say the Formula 1 champion was showing surprising improvement that allowed a second surgery for head injuries he suffered during a ski accident, but cautioned that his brain still had extensive bruising.

Schumacher was skiing with his son when he fell and struck a rock Sunday in the French Alps.

"There are hematomes a little bit everywhere," said Dr. Emmanuel Gay, describing the extensive bruising throughout Schumacher's brain. But Gay said surgeons decided upon a second operation after Schumacher's unexpected, though small, improvement on Monday.

They offered no predictions Tuesday on whether or when they would bring him out of an induced coma, intended to relieve swelling.

"We cannot tell you any more on the future," said Gerard Saillant, a surgeon and friend of the family.

The German driver was skiing with his son Sunday morning in the French Alpine resort of Meribel when he fell and hit the right side of his head on a rock. He was wearing a helmet, but doctors said it was not enough to prevent a serious brain injury.

Gerard Saillant, a trauma surgeon who operated on Schumacher when he broke his leg in a 1999 race crash, was at the hospital as a visitor. He told reporters that Schumacher's age — he turns 45 on Jan. 3 — and his fitness should work in his favor.

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The neurology team at Grenoble University Hospital is recognized as among the best in France and the hospital, in a city that is the gateway to the French Alps, sees a large number of skiing accidents every year.

Schumacher has been seriously hurt before. He broke his leg in a crash at the Silverstone race course in 1999. He also suffered serious neck and spine injuries after a motorcycling accident in February 2009 in Spain.

The area where Schumacher was skiing is part of a web of trails that slice down through a vast and, in parts, very steep snowfield. Although challenging, the snowfield is not extreme skiing. The runs are broad and neatly tended, and the ungroomed area in between, known as off-piste — where the resort said Schumacher was found — is free of trees.

His wife and other family members were by his bedside.

As news of the accident spread, Formula One drivers and fans rushed to wish Schumacher a quick recovery.

"Like millions of Germans, the chancellor and members of the government were extremely dismayed when they heard about Michael Schumacher's serious skiing accident," German Chancellor Angela Merkel's spokesman, Steffen Seibert, said in Berlin.

Sebastian Vettel, for whom Schumacher was a boyhood idol, told German news agency dpa: "I am shocked and hope that he will get better as soon as possible."

Ferrari, which Schumacher raced for, expressed its concern in a statement.

"Everyone at Ferrari has been in a state of anxiety since hearing about Michael Schumacher's accident," it said, adding that company president, Luca di Montezemolo, and race team leader, Stefano Domenicali, were in contact with the family.

British former world champion Jenson Button said posted that his "thoughts are with Michael Schumacher at this tough time. ... Michael more than anyone has the strength to pull through this."

During his career, Schumacher won seven drivers' championships and 91 race wins. After initial success with the Benetton team, Schumacher moved to Ferrari and helped turn the Italian team into the sport's dominant force. After initially retiring in 2006, he made a comeback in 2010 and raced for three years with Mercedes.